Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class A {

    public static void main(String[] args) throws NumberFormatException,
            IOException {
        BufferedReader buf = new BufferedReader(
                new InputStreamReader(System.in));
        int n = Integer.parseInt(buf.readLine());
        n *= 2;
        int x = 1;
        boolean yes = false;
        
        while (x < n && !yes) {
            int y = x * (x + 1);
            int z = n - y;
            if (z <= 0)
                break;
            int w = (int) Math.sqrt(z);
            if (w * (w + 1) == z)
                yes = true;
            x++;
        }
        if (yes)
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}